Find the probability of at most two tails or at least two heads in a toss of three coins.
Answer
363.6k+ views
Hint: Here we proceed the solution by considering all possible outcomes of three coins when they are tossed. So here we have to find the probability of at most two tails or at least two heads where at most indicates two or less than two.
Complete step-by-step answer:
Let set S be the sample space of all three possible outcomes of three coins tossed.
S= {HHH, HTH, THH, HHT, TTH, HTT, THT, TTT}
Here H denotes Heads and T denotes Tail
Now from the set S
The total number of outcomes = 8
Here we have to find probability of at most two tails or at least two heads
As we know that at most 2 means two or less than two. So now by using the at most condition, we can say
Number of outcomes with at-most two tails or at least two heads = 7
Now by using the total number of outcomes and number of outcomes with at-most two tails or at-least two heads we can find the required probability.
Therefore probability of at-most two tails and at least two in a toss of three coins =
$
= \dfrac{{{\text{Number of outcomes with at most 2tails or at least 2heads}}}}{{{\text{total number of outcomes}}}} \\
= \dfrac{7}{8} \\
$
Note: In this problem we have to focus on two words they are at-most and at-least these are the two key words the whole problem depends on these are conditions these are conditions given to solve the problem. Generally everyone will ignore these words which will affect the answer.
Complete step-by-step answer:
Let set S be the sample space of all three possible outcomes of three coins tossed.
S= {HHH, HTH, THH, HHT, TTH, HTT, THT, TTT}
Here H denotes Heads and T denotes Tail
Now from the set S
The total number of outcomes = 8
Here we have to find probability of at most two tails or at least two heads
As we know that at most 2 means two or less than two. So now by using the at most condition, we can say
Number of outcomes with at-most two tails or at least two heads = 7
Now by using the total number of outcomes and number of outcomes with at-most two tails or at-least two heads we can find the required probability.
Therefore probability of at-most two tails and at least two in a toss of three coins =
$
= \dfrac{{{\text{Number of outcomes with at most 2tails or at least 2heads}}}}{{{\text{total number of outcomes}}}} \\
= \dfrac{7}{8} \\
$
Note: In this problem we have to focus on two words they are at-most and at-least these are the two key words the whole problem depends on these are conditions these are conditions given to solve the problem. Generally everyone will ignore these words which will affect the answer.
Last updated date: 29th Sep 2023
•
Total views: 363.6k
•
Views today: 9.63k
Recently Updated Pages
What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

One cusec is equal to how many liters class 8 maths CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE
